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Algebraic groups are treated in this volume from a group theoretical point of view and the obtained results are compared with the analogous issues in the theory of Lie groups. The main body of the text is devoted to a classification of algebraic groups and Lie groups having only few subgroups or few factor groups of different type. In particular, the diversity of the nature of algebraic groups over fields of positive characteristic and over fields of characteristic zero is emphasized. This is revealed by the plethora of three-dimensional unipotent algebraic groups over a perfect field of positive characteristic, as well as, by many concrete examples which cover an area systematically. In the final section, algebraic groups and Lie groups having many closed normal subgroups are determined.

Linear algebraic groups. --- Lie groups. --- Group theory. --- Groupes linéaires algébriques --- Groupes de Lie --- Groupes, Théorie des --- Linear algebraic groups --- Lie groups --- Group theory --- Geometry --- Algebra --- Mathematical Theory --- Mathematics --- Physical Sciences & Mathematics --- Théorie des groupes --- Groups, Theory of --- Substitutions (Mathematics) --- Groups, Lie --- Algebraic groups, Linear --- Mathematics. --- Algebraic geometry. --- Nonassociative rings. --- Rings (Algebra). --- Topological groups. --- Group Theory and Generalizations. --- Algebraic Geometry. --- Topological Groups, Lie Groups. --- Non-associative Rings and Algebras. --- Lie algebras --- Symmetric spaces --- Topological groups --- Groups, Topological --- Continuous groups --- Algebraic rings --- Ring theory --- Algebraic fields --- Rings (Algebra) --- Algebraic geometry --- Math --- Science --- Geometry, Algebraic --- Algebraic varieties --- Geometry, algebraic. --- Topological Groups. --- Algebra. --- Mathematical analysis

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Algebraic groups are treated in this volume from a group theoretical point of view and the obtained results are compared with the analogous issues in the theory of Lie groups. The main body of the text is devoted to a classification of algebraic groups and Lie groups having only few subgroups or few factor groups of different type. In particular, the diversity of the nature of algebraic groups over fields of positive characteristic and over fields of characteristic zero is emphasized. This is revealed by the plethora of three-dimensional unipotent algebraic groups over a perfect field of positive characteristic, as well as, by many concrete examples which cover an area systematically. In the final section, algebraic groups and Lie groups having many closed normal subgroups are determined.

Group theory --- Ordered algebraic structures --- Topological groups. Lie groups --- Geometry --- algebra --- landmeetkunde --- topologie (wiskunde) --- wiskunde